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Strong base for fuzzy topology


It is known that a base for a traditional topology, or for a $L$-topology, $\tau$, is a subset ${\mathcal B}$ of $\tau$ with the property that every element $G\in \tau$ can be written as a union of elements of ${\mathcal B}$. In the classical case it is equivalent to say that $G\in \tau$ if and only if for any $x\in G$ we have $B\in {\mathcal B}$ satisfying $x\in B \subseteq G$. This latter property is taken as the foundation for a notion of strong base for a $L$-topology. Characteristic properties of a strong base are given and among other results it is shown that a strong base is a base, but not conversely.

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TitleStrong base for fuzzy topology
SourceMethods Funct. Anal. Topology, Vol. 17 (2011), no. 4, 350-355
MathSciNet   MR2907363
CopyrightThe Author(s) 2011 (CC BY-SA)

Authors Information

A. A. Rakhimov
Tashkent Institute of Railways and Engineering, Tashkent, Uzbekistan; Karadeniz Technical University, Turkey

F. M. Zakirov
Tashkent Autoroad Institute, Tashkent, Uzbekistan 

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A. A. Rakhimov and F. M. Zakirov, Strong base for fuzzy topology, Methods Funct. Anal. Topology 17 (2011), no. 4, 350-355.


@article {MFAT582,
    AUTHOR = {Rakhimov, A. A. and Zakirov, F. M.},
     TITLE = {Strong base for fuzzy topology},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {17},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {350-355},
      ISSN = {1029-3531},
  MRNUMBER = {MR2907363},
       URL = {},

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